Question

Expand the following and verify:
(a + b + c)² = (-a-b-ch?^2
(-a +b+c) = (a – 6-c)?
(a - b + c)2 = (-a +b-cl?
(a + b - c) = (-a - b+c)​

Answer 1

Answer:

Now we will learn to expand the square of a trinomial (a + b + c).

Let (b + c) = x

Then (a + b + c)2 = (a + x)2 = a2 + 2ax + x2

= a2 + 2a (b + c) + (b + c)2

= a2 + 2ab + 2ac + (b2 + c2 + 2bc)

= a2 + b2 + c2 + 2ab + 2bc + 2ca

Therefore, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Answer 2

Step-by-step explanation:

(a + b + c)² = (-a-b-c)²

a²+b²+c²+2ab+2bc+2ca=a²+b²+c²+2ab+2bc+2ca

L.H.S = R.H.S

HENCE PROVED

(-a +b+c) = (a -b-c)²

a²+b²+c²-2ab+2bc-2ca=a²+b²+c²-2ab+2bc-2ca

L.H.S = R.H.S

HENCE PROVED

(a - b + c)² = (-a +b-c)²

a²+b²+c²-2ab-2bc+2ca=a²+b²+c²-2ab-2bc+2ca

L.H.S = R.H.S

HENCE PROVED

(a + b - c)²= (-a - b+c)²

a²+b²+c²+2ab-2bc-2ca=a²+b²+c²+2ab-2bc-2ca

L.H.S = R.H.S

HENCE PROVED

..ALL ARE EQUAL..